Section B: Statistics [60 marks] A company wants to find out the transportation habits of their employees. On one particular workday, the interviewer selects a sample of employees to interview from those walking into the company building by

• standing at the entrance of building and choosing at random one of the first 10 employees who walks into the building,
• then choosing every 10th employee after the first employee is chosen.

1. Identify the sampling method from the given description

The method involves selecting a random starting point among the first $10$ employees and then picking every $10$th employee thereafter. This defines systematic sampling.

1. State a context-specific disadvantage of systematic sampling.

A key disadvantage of systematic sampling is its vulnerability to periodic patterns in the population. In this context, employees arriving by the same transport mode (like a bus or train) might enter the building in groups at regular intervals. Choosing every 10th person might consistently pick people from these same groups or miss them entirely, leading to a biased representation of transportation habits.

(Alternatively, practically, it may be difficult for the interviewer to accurately keep track of every 10th employee during the morning peak hour when many employees walk in at the same time).

1. State the division of the population into categories and the setting of quotas.

The interviewer divides the population of employees into mutually exclusive categories (for example, by gender or department) and sets a specific quota for each category such that the total number of employees to be selected adds up to $30$.

2. Explain the non-random selection process to fulfil the quotas.

The interviewer then stands at the entrance and approaches employees non-randomly (e.g., choosing the first individuals available who fit the required categories) and stops interviewing once the quota for every category has been exactly fulfilled.